Sampling recovery in 𝐿₂ and other norms

We study the recovery of functions in various norms, including L p L_p with 1 ≤ p ≤ ∞ 1≤ p≤ ∞ , based on function evaluations. We obtain worst case error bounds for general classes of functions in terms of the best L 2 L_2 -approximation from a given nested sequence of subspaces and the Christoffel function of these subspaces. In the case p = ∞ p=∞ , our results imply that linear sampling algorithms are optimal up to a constant factor for many reproducing kernel Hilbert spaces.